Question: Solve for $x$ and $y$ using elimination. $\begin{align*}7x-4y &= 5 \\ 3x-3y &= -3\end{align*}$
Explanation: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-3$ and the bottom equation by $4$ $\begin{align*}-21x+12y &= -15\\ 12x-12y &= -12\end{align*}$ Add the top and bottom equations. $-9x = -27$ Divide both sides by $-9$ and reduce as necessary. $x = 3$ Substitute $3$ for $x$ in the top equation. $7( 3)-4y = 5$ $21-4y = 5$ $-4y = -16$ $y = 4$ The solution is $\enspace x = 3, \enspace y = 4$.